Generalized Solutions of Operator Equations and Ex
Klyushin, D.A.; Lyashko, S.I.; Nomirovskii, D.A.; Petunin, Yu.I.; Semenov, Vladimir
ISBN 10: 1461406188 ISBN 13: 9781461406181
Editorial: Springer, 2011
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Sinopsis:
Preface1. Fundamental notions, general and auxiliary facts2. Simplest schemes of generalized solution of linear operator equations2.1. Strong generalized solution2.2. Strong almost solution2.3. Weak generalized solution2.4. Weak almost solution2.5. Unique existence of weak generalized solution2.6. Relationship between weak and strong generalized solutions3. A priori estimations for linear continuous operator3.1. A priori inequalities3.2. Generalized solution of operator equation in Banach spaces3.3. Generalized solution of operator equation in locally convex topological spaces3.4. Relationship between generalized solutions in Banach and locally convex topological spaces4. Applications of the theory of generalized solvability of linear equations4.1. Equations with Hilbert-Schmidt operator in Hilbert space L2(-,)4.2. Generalized solution of infinite system of linear algebraic equations4.3. Volterra Integral Equation of the First Kind4.4. Statistics of random processes4.5. Parabolic PDE in a connected domain4.6. Parabolic PDE in a disconnected domain5. Scheme of generalized solutions of linear operator equations5.1. Generalized solution of linear operator equations in locally convex linear topological spaces5.2. Examples of generalized solutions5.3. Properties of generalized solutions in spaces E1, E26. Scheme of generalized solutions of nonlinear operator equations6.1. Generalized solution of nonlinear operator equation6.2. Almost solution of nonlinear operator equations6.3. Unique existence of generalized solution6.4. Correctness of generalized solutions6.5. Pseudo-generalized and essentially generalized solutions6.6. Embedding of space of pseudo-generalized solutions into space of generalized solutions6.7. Examples of operators6.8. Computation of generalized solution7. Generalized extreme elements7.1. Examples of generalized extreme elements7.2. Generalized extreme elements for linear and positively homogeneous convex functional7.3. Generalized extreme elements for general convex functional7.4. Some remarksReference
De la contraportada:
The abstract models for many problems in science and engineering take the form of an operator equation; the resolution of these problems often requires determining the existence and uniqueness of solutions to these equations. Generalized Solutions of Operator Equations and Extreme Elements presents a general functional analytic approach to solving operator equations in a general form. This unique and valuable monograph presents recently obtained results in the study of the generalized solutions of operator equations and extreme elements in linear topological spaces. The results are clearly and thoroughly presented and offer new methods of identifying these solutions and studying their properties. These methods are based on a priori estimations and a general topological approach to construct generalized solutions of linear and nonlinear operator equations.
This volume is intended for mathematicians, graduate students and researchers studying functional analysis, operator theory, and the theory of optimal control. Prerequisites include knowledge of basic functional analysis.
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Detalles bibliográficos
Título: Generalized Solutions of Operator Equations ...
Editorial: Springer
Año de publicación: 2011
Encuadernación: Encuadernación de tapa dura
Condición: Brand New